For , consider the family of functions . At , the derivative exists under which of…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For m>0m>0, consider the family of functions gm(x)=∣x∣mg_m(x)=|x|^{m}. At x=0x=0, the derivative gm′(0)g_m'(0) exists under which of the following conditions on mm? (a) It exists only when m≥1m\ge 1. (b) It exists only when m>1m>1. (c) It exists only when m=1m=1. (d) It exists only when 0<m<10<m<1.

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